Examples

PT1/low-pass filter step response

Code: Creating a transfer function and plotting its response

T1=0.4;# time constantP=tf([1],[T11])# create transfer function modelstep(P,2)# plot step response#add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1holdonplot([0T1],[01],"g")plot([T1T1],[01],"k")plot([0T1],[1-1/e1-1/e],"m")holdoff

Try also bode(P)!
(a first order low-pass filter has -3db magnitude at f=1/T1)

Linearization around the point θ=π{\textstyle \theta =\pi } and substitution of θ′=θ−π{\textstyle \theta '=\theta -\pi } (from here on in the analysis, θ′{\textstyle \theta '} will be written as θ{\textstyle \theta }, but it should be noted that θ{\textstyle \theta } now
measures from a new reference) leads to